Advantages of E.R. Model
Exceptional conceptual simplicity
Visual representation
Effective communication tool
Integrated with the relational data model
Disadvantages of E.R. Model
Limited constraint representation
Limited relationship representation
No data manipulation language
Loss of information content
‫عناصر ال‪ERD‬‬
‫•‬
‫‪1) Entity Set‬‬
‫‪ OOP‬وهو الكائن مثل مفهومه في ال‬
‫ويتم وضعها في التصميم على شكل مستطيل‬
‫‪Examples: a computer, an employee, a song, a mathematical theorem. Entities‬‬
‫‪are represented as rectangles.‬‬
‫‪2) attribute‬‬
‫وهو خواص ال كائن‬
‫وياخذ الشكل البيضاوى‬
‫‪3) Primary key‬‬
‫المستخدم ك مفتاح أساسى ‪ attribute‬يتم وضع خط تحت ال‬
‫‪4) Relationship‬‬
‫‪2 entities‬العالقات ‪ ،‬وهى تحدد كيفية اتصال‬
‫‪ diamond‬مع بعضهم ‪ ،‬وهى تأخذ شكل الماسي‬
‫• و في اغلب االحيان يكون اسم الكيان اسما ً مفردا‬
‫• امثلة على الكيان ‪ :‬مريض ‪ ،‬دواء ‪ ،‬يعالج بـ ‪.‬‬
‫• العالقة الرابطة“‪ :“Relationships‬هي العالقة التي تربط‬
‫بين الكيانات و تمثل رابطة العالم المصغر الذي تمثله قاعدة‬
‫البيانات‪.‬‬
‫• تعبر العالقات الرابطة عن الروابط بين البيانات في الواقع و‬
‫تمثل في اغلب االحوال بفعل مضارع او فعالً مبني للمجهول‬
‫• امثلة على العالقات الرابطة‬
‫– الكيان طالب و الكيان مدرس و مقرر دراسي يوجد بينهم عدة‬
‫عالقات رابطه منها‬
‫•‬
‫•‬
‫•‬
‫•‬
‫الطالب يدرس مقرر درسي‬
‫المدرس يُدرس المقرر الدراسي‪.‬‬
‫المدرس يُدرس الطالب المقرر الدراسي ‪.‬‬
‫المدرس يرشد الطالب الى المقرر المناسب‪.‬‬
‫• الطالب يُرشد بواسطة المدرس‬
‫• انواع الروابط بين عناصر البيانات‬
‫– رابطة واحدة ‪ :One Association‬رابطة بين عنصرين تعني آن كل عنصر بيانات‬
‫من خاصية ما يقابلها عنصر بيانات واحد من العنصر الثاني (كل رقم طالب يقابله اسم‬
‫طالب واحد )‬
‫رقم الطالب‬
‫‪1‬‬
‫اسم الطالب‬
‫‪1:1‬‬
‫– رابطة متعددة ‪ : Many Association‬رابطة بين عنصرين تعني ان كل عنصر‬
‫بيانات من خاصية ما يقابلها عناصر بيانات متعددة من العنصر الثاني (كل رقم طالب‬
‫يقابله اكثر من مقرر مادة )‬
‫المقرر‬
‫رقم الطالب‬
‫‪1‬‬
‫‪1:N‬‬
‫– رابطة كاردينالتي (‪)Cardinal Association‬‬
‫– نوع الرابطة هنا يتداخل مع الرابطة الواحدة و الرابطة المتعددة‬
‫• مع الرابطة الواحدة تحدد نسبة ‪ 0:1‬اي من صفر الى واحد مثل الرابط بين رقم السرير و رقم‬
‫المريض‬
‫» مع الرابطة المتعددة تحدد نسبة ‪ 0:N‬اي من صفر الى واحد مثل الرابط بين رقم السرير و رقم‬
‫المريض‬
‫طبعا ممكن ان تكون النسبة ‪ 1‬بدل صفر في جميع االمثلة اعاله‬
‫»‬
‫•‬
‫رقم المريض‬
‫‪0‬‬
‫‪0:1‬‬
‫رقم السرير‬
‫رقم المريض‬
‫‪0‬‬
‫‪0:N‬‬
‫رقم الغرفة‬
What is the relationships?
• Relationships can be thought of as verbs, linking
two or more nouns. Examples: an owns
relationship between a company and a
computer, a supervises relationship between an
employee and a department, a performs
relationship between an artist and a song, a
proved relationship between a mathematician
and a theorem. Relationships are represented as
diamonds, connected by lines to each of the
entities in the relationship
ER diagram ForSchool
Explanation of the previous example
•
we have 5 entities
teacher
student
subject
group
Mark
‫ كل منهما له‬attributes
‫وما تحته خط هو المفتاح األساسي‬
‫ عالقات‬3 ‫ولدينا‬
‫منهما‬
2 ‫ عالقة ثنائية " ما بين‬entities "
belong
3 ‫ وعالقتين ثالثية " ما بين‬entities
give
supervises
Car rent
Train teckets
Data anomalies problem
‫مشكلة تكرار البيانات‬
Adding problems : we cant add new department unless it
as employee because the primary key is Empno
Updating and deleting problem : to update the Loc field
from jeddah to riadh for one employee will corapt the
other employee locations
To solve those problems
•
•
•
•
•
•
•
Function dependency FD -
A- B
Means B is depending Functionally on A
I.e A value define B value
Example:
For each empl. Only unique name
For each empl. Only unique dept
•
•
•
•
•
FD1: Empno Ename
FD2: Empno Deptno
We can write it as:
FD1: Empno Ename,Deptno
FD :Functional Dependency
Basic Structure
• Formally, given sets D1, D2, …. Dn a relation r is a subset of
D 1 x D2 x … x Dn
Thus a relation is a set of n-tuples (a1, a2, …, an) where
each ai  Di
• Example: if
customer-name = {Jones, Smith, Curry, Lindsay}
customer-street = {Main, North, Park}
customer-city = {Harrison, Rye, Pittsfield}
Then r  customer-name x customer-street x customer-city
r = { (Jones, Main, Harrison),
(Smith, North, Rye),
(Curry, North, Rye),
(Lindsay, Park, Pittsfield)}
is a relation over customer-name x customer-street x customer-city
Attribute Types
• Each attribute of a relation has a name
• The set of allowed values for each attribute is called
the domain of the attribute
• Attribute values are (normally) required to be atomic,
that is, indivisible
– E.g. multivalued attribute values are not atomic
– E.g. composite attribute values are not atomic
• The special value null is a member of every domain
• The null value causes complications in the definition of
many operations
– we shall ignore the effect of null values in our main
presentation and consider their effect later
Relation Schema
• A1, A2, …, An are attributes
• R = (A1, A2, …, An ) is a relation schema
E.g. Customer-schema =
(customer-name, customer-street,
customer-city)
• r(R) is a relation on the relation schema R
E.g. customer (Customer-schema)
Relation Instance
• The current values (relation instance) of a
relation are specified by a table
• An element t of r is a tuple, represented by a
attributes
row in a table
(or columns)
customer-name
customer-street
customer-city
Jones
Smith
Curry
Lindsay
Main
North
North
Park
Harrison
Rye
Rye
Pittsfield
customer
tuples
(or rows)
Determining Keys from E-R Sets
• Strong entity set. The primary key of the entity set
becomes the primary key of the relation.
• Weak entity set. The primary key of the relation consists of
the union of the primary key of the strong entity set and
the discriminator of the weak entity set.
• Relationship set. The union of the primary keys of the
related entity sets becomes a super key of the relation.
– For binary many-to-one relationship sets, the primary key of the
“many” entity set becomes the relation’s primary key.
– For one-to-one relationship sets, the relation’s primary key can
be that of either entity set.
– For many-to-many relationship sets, the union of the primary
keys becomes the relation’s primary key
Schema Diagram for the Banking Enterprise
Normalization
An update anomaly
An update anomaly. Employee 519 is shown as
having different addresses on different records.
insertion anomaly
An insertion anomaly. Until the new faculty member,
Dr. Newsome, is assigned to teach at least one course,
his details cannot be recorded.
A deletion anomaly
A deletion anomaly. All information about Dr. Giddens is
lost when he temporarily ceases to be assigned to any
courses.
Query Languages
• Language in which user requests information from the
database.
• Categories of languages
– procedural
– non-procedural
• “Pure” languages:
– Relational Algebra
– Tuple Relational Calculus
– Domain Relational Calculus
• Pure languages form underlying basis of query
languages that people use.
Relational Algebra
• Procedural language
• Six basic operators
–
–
–
–
–
–
select
project
union
set difference
Cartesian product
rename
• The operators take two or more relations as
inputs and give a new relation as a result.
Select Operation – Example
• Relation r
• A=B ^ D > 5 (r)
A
B
C
D


1
7


5
7


12
3


23 10
A
B
C
D


1
7


23 10
Select Operation
• Notation:  p(r)
• p is called the selection predicate ‫االختيار المبنى عليه‬
• Defined as:
p(r) = {t | t  r and p(t)}
Where p is a formula in propositional calculus
consisting of terms connected by :  (and),  (or), 
(not)
Each term is one of:
<attribute> op
<attribute> or
<constant>
where op is one of: =, , >, . <. 
• Example of selection:
p(r) ‫ تمثل‬ branch-name=“Perryridge”(account)
Relational Model algebra
• Structure of Relational Databases
• Relational Algebra
• Tuple Relational Calculus ‫العالقات المضاعفة‬
‫الحسابية‬
• Domain Relational Calculus
• Extended Relational-Algebra-Operations
• Modification of the Database
• Views
Projection Operation
• Given a relation R, the projection operation is
used to create a new relation S, such that each
tuple ts is formed by taking a tuple tR and
removing one or more columns.
• Formally, the projection of R over columns A1,
A2, …,An is defined as:
S   A1 , A2 ,..., An ( R)
 {ts  ( A1 , A2 ,..., An ) | t R  R, t R  ( B1 , B2 ,..., Bk ),
and { A1 , A2 ,..., An }  {B1 , B2 ,..., Bk }}
Project Operation – Example
• Relation r:
 ∏A,C (r)
A
B
C

10
1

20
1

30
1

40
2
A
C
A
C

1

1

1

1

1

2

2
=
Project Operation
• Notation: ‫الحظ ان‬
A1, A2, …, Ak (r)
where A1, A2 are attribute names and r is a relation
name.
• The result is defined as the relation of k columns
obtained by erasing the columns that are not listed
• Duplicate rows removed from result, since relations are
sets
• E.g. To eliminate the branch-name attribute of account
account-number, balance (account)
Data anomalies
• What is the problem of this DB table?
• 1- adding, deleting and updating problems
• Adding prob: We cant add new dept without Empno because
the prim key is Empno
• 2-redandance in data of Dname and Loc, so if we changed Lc from
jeddah to riyadh for one Emp, will must change for all Emp
‫‪FD rules‬‬
‫تعنى انه إذا تحقق ما قبلها فإنه يمكن استنتاج الجانب اآلخر =|‬
‫قاعدة االنعكاس ‪1- reflection rule‬‬
‫‪If Y is a part of X ‬‬
‫‪Then XY‬‬
‫)‪ X‬تحدد قيمة ‪( Y‬‬
‫قاعدة اإلضافة ‪2- Augmentation rule‬‬
‫‪{XY} |= XZYZ‬‬
‫•‬
‫•‬
‫•‬
‫•‬
‫•‬
‫•‬
‫قاعدة التعدي ‪• 3- Transitive‬‬
‫‪• { XY , Y Z} |= XZ‬‬
‫• اذا كانت ‪ X‬تحدد ‪ Y‬و كانت ‪Y‬تحدد ‪ Z‬فإن ‪X‬تحدد ‪Z‬‬
‫‪• 4- Union‬‬
‫االتحاد‬
‫‪• { XY , X Z} |= XYZ‬‬
‫• اذا كانت ‪ X‬تحدد ‪ Y‬و كانت ‪X‬تحدد ‪ Z‬فإن ‪X‬تحدد ‪ZY‬‬
Union Operation – Example
•
Relations r, s:
A
B
A
B

1

2

2

3

1
s
r
r U s:
A
B

1

2

1

3
Union Operation
 Notation: r  s
 Defined as:
r  s = {t | t  r or t  s}
 For r  s to be valid.
1. r, s must have the same arity (same number of attributes)
2. The attribute domains must be compatible (e.g., 2nd column
of r deals with the same type of values as does the 2nd
column of s)
 E.g. to find all customers with either an account or a loan
customer-name (depositor)  customer-name (borrower)
Set Difference Operation – Example
•
Relations r, s:
A
B
A
B

1

2

2

3

1
s
r
r – s:
A
B

1

1
Set Difference Operation
• Notation r – s
• Defined as:
r – s = {t | t  r and t  s}
• Set differences must be taken between
compatible relations.
– r and s must have the same arity
– attribute domains of r and s must be compatible
Cartesian-Product Operation-Example
Relations r, s:
A
B
C
D
E

1

2




10
10
20
10
a
a
b
b
r
s
r x s:
A
B
C
D
E








1
1
1
1
2
2
2
2








10
10
20
10
10
10
20
10
a
a
b
b
a
a
b
b
Cartesian-Product Operation
• Notation r x s
• Defined as:
r x s = {t q | t  r and q  s}
• Assume that attributes of r(R) and s(S) are disjoint.
(That is,
R  S = ).
• If attributes of r(R) and s(S) are not disjoint, then
renaming must be used.
• A tuple is r x s is made by concatenating the columns
from the first tuple, with the those of the second tuple.
Composition of Operations
• Can build expressions using multiple operations
• Example: A=C(r x s)
A B C D E
• rxs
 1  10 a
• A=C(r x s)







1
1
1
2
2
2
2







10
20
10
10
10
20
10
a
b
b
a
a
b
b
A
B
C
D
E



1
2
2
 10
 20
 20
a
a
b
Rename Operation
• Allows us to name, and therefore to refer to, the
results of relational-algebra expressions.
• Allows us to refer to a relation by more than one name.
Example:
 x (E)
returns the expression E under the name X
If a relational-algebra expression E has arity n, then
x (A1, A2, …, An) (E)
returns the result of expression E under the name X, and
with the
attributes renamed to A1, A2, …., An.
•
•
•
•
•
5- Decomposition ‫التقسيم‬
Is the opposite of Union
{XYZ } |= XY
6- pseudo transitive ‫التعدي الزائف‬
{XY, WYZ} |= WXY
Example
• The PK related to a complex table which is not
allowed, so me must simplify the table
Example
• Every field contain more than one vaue, so we
must simplify them.
• But we have another problem, the redundancy of
PK with different instancesin deptno,
project_code, Dname,…
• So we must use relation algebra to distinguish
new PK
• FD 1 :No Name
• According to the previous relation we can see
it follow the 1NF(first normal form)
Banking Example
branch (branch-name, branch-city, assets)
customer (customer-name, customer-street,
customer-only)
account (account-number, branch-name, balance)
loan (loan-number, branch-name, amount)
depositor (customer-name, account-number)
borrower (customer-name, loan-number)
Example Queries
•
Find all loans of over $1200
amount > 1200 (loan)
Find the loan number for each loan of an amount greater than
$1200
loan-number (amount > 1200 (loan))
Example Queries
• Find the names of all customers who have a loan, an
account, or both, from the bank
customer-name (borrower)  customer-name (depositor)
Find the names of all customers who have a loan and an
account at bank.
customer-name (borrower)  customer-name (depositor)
Example Queries
• Find the names of all customers who have a loan at
the Perryridge branch.
customer-name (branch-name=“Perryridge”
(borrower.loan-number = loan.loan-number(borrower x loan)))
 Find the names of all customers who have a loan at the
Perryridge branch but do not have an account at any branch of
the bank.
customer-name ( branch-name = “Perryridge”
( borrower.loan-number = loan.loan-number(borrower x loan))) –
customer-name(depositor)
Example Queries
• Find the names of all customers who have a loan at the
Perryridge branch. Two possible solutions follow:
Query 1
customer-name(branch-name = “Perryridge” (
borrower.loan-number = loan.loan-number(borrower x loan)))
 Query 2
customer-name(loan.loan-number = borrower.loan-number(
(branch-name = “Perryridge”(loan)) x borrower))
Example Queries
Find the largest account balance
• Rename account relation as d
• The query is:
balance(account) - account.balance
(account.balance < d.balance (account x d (account)))